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<h1><a
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
height="100"></a> Qhull Geomview options (G)</h1>

This section lists the Geomview options for Qhull. These options are
indicated by 'G' followed by a letter.  See
<a href="qh-opto.htm#output">Output</a>, <a href="qh-optp.htm#print">Print</a>,
and <a href="qh-optf.htm#format">Format</a> for other output options.


<p><b>Copyright &copy; 1995-2020 C.B. Barber</b></p>

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<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
<a name="geomview">&#149;</a> <a href="qh-quick.htm#options">Options</a>
&#149; <a href="qh-opto.htm#output">Output</a>
&#149; <a href="qh-optf.htm#format">Formats</a>
&#149; <a href="qh-optg.htm#geomview">Geomview</a>
&#149; <a href="qh-optp.htm#print">Print</a>
&#149; <a href="qh-optq.htm#qhull">Qhull</a>
&#149; <a href="qh-optc.htm#prec">Precision</a>
&#149; <a href="qh-optt.htm#trace">Trace</a>
&#149; <a href="http://www.qhull.org/src/libqhull_r/index.htm">Functions</a> (<a href="../src/libqhull_r/index.htm">local</a>)</p>

<h2>Geomview output options</h2>

<p><a href="http://www.geomview.org">Geomview</a> is the graphical
viewer for visualizing Qhull output in 2-d, 3-d and 4-d.</p>

<p>Geomview displays each facet of the convex hull. The color of
a facet is determined by the coefficients of the facet's normal
equation. For imprecise hulls, Geomview displays the inner and
outer hull. Geomview can also display points, ridges, vertices,
coplanar points, and facet intersections. </p>

<p>For 2-d Delaunay triangulations, Geomview displays the
corresponding paraboloid.  Geomview displays the 2-d Voronoi
diagram. For halfspace intersections, it displays the
dual convex hull. </p>

<dl compact>
    <dt><a href="#G">G</a></dt>
    <dd>display Geomview output</dd>
    <dt><a href="#GDn">GDn</a></dt>
    <dd>drop dimension n in 3-d and 4-d output </dd>
    <dt><a href="#Gt">Gt</a></dt>
    <dd>display transparent 3-d Delaunay triangulation</dd>

    <dt>&nbsp;</dt>
    <dt>&nbsp;</dt>
    <dd><b>Specific</b></dd>
    <dt><a href="#Ga">Ga</a></dt>
    <dd>display all points as dots</dd>
    <dt><a href="#Gc">Gc</a></dt>
    <dd>display centrums (2-d, 3-d)</dd>
    <dt><a href="#Gh">Gh</a></dt>
    <dd>display hyperplane intersections</dd>
    <dt><a href="#Gi">Gi</a></dt>
    <dd>display inner planes only (2-d, 3-d)</dd>
    <dt><a href="#Gn">Gn</a></dt>
    <dd>do not display planes</dd>
    <dt><a href="#Go">Go</a></dt>
    <dd>display outer planes only (2-d, 3-d)</dd>
    <dt><a href="#Gp">Gp</a></dt>
    <dd>display coplanar points and vertices as radii</dd>
    <dt><a href="#Gr">Gr</a></dt>
    <dd>display ridges (3-d)</dd>
    <dt><a href="#Gv">Gv</a></dt>
    <dd>display vertices as spheres</dd>

</dl>

<hr>

<h3><a href="#geomview">&#187;</a><a name="G">G - produce output for
viewing with Geomview</a></h3>

<p>By default, option 'G' displays edges in 2-d, outer planes in
3-d, and ridges in 4-d.</p>

<p>A ridge can be explicit or implicit. An explicit ridge is a <i>(d-1)</i>-dimensional
simplex between two facets. In 4-d, the explicit ridges are
triangles. An implicit ridge is the topological intersection of
two neighboring facets. It is the union of explicit ridges.</p>

<p>For non-simplicial 4-d facets, the explicit ridges can be
quite complex. When displaying a ridge in 4-d, Qhull projects the
ridge's vertices to one of its facets' hyperplanes. Use '<a
href="#Gh">Gh</a>' to project ridges to the intersection of both
hyperplanes. This usually results in a cleaner display. </p>

<p>For 2-d Delaunay triangulations, Geomview displays the
corresponding paraboloid.  Geomview displays the 2-d Voronoi
diagram. For halfspace intersections, it displays the
dual convex hull.

<h3><a href="#geomview">&#187;</a><a name="Ga">Ga - display all points as dots</a></h3>

<p>Each input point is displayed as a green dot.</p>

<h3><a href="#geomview">&#187;</a><a name="Gc">Gc - display centrums (3-d)</a></h3>

<p>The centrum is defined by a green radius sitting on a blue
plane. The plane corresponds to the facet's hyperplane. If you
sight along a facet's hyperplane, you will see that all
neighboring centrums are below the facet. The radius is defined
by '<a href="qh-optc.htm#Cn">C-n</a>' or '<a
href="qh-optc.htm#Cn2">Cn</a>'.</p>

<h3><a href="#geomview">&#187;</a><a name="GDn">GDn - drop dimension n in 3-d and 4-d output</a></h3>

<p>The result is a 2-d or 3-d object. In 4-d, this corresponds to
viewing the 4-d object from the nth axis without perspective.
It's best to view 4-d objects in pieces. Use the '<a
href="qh-optp.htm#Pdk">Pdk</a>' '<a href="qh-optp.htm#Pg">Pg</a>'
'<a href="qh-optp.htm#PG">PG</a>' '<a href="qh-optq.htm#QGn">QGn</a>'
and '<a href="qh-optq.htm#QVn">QVn</a>' options to select a few
facets. If one of the facets is perpendicular to an axis, then
projecting along that axis will show the facet exactly as it is
in 4-d. If you generate many facets, use Geomview's <tt>ginsu</tt>
module to view the interior</p>

<p>To view multiple 4-d dimensions at once, output the object
without 'GDn' and read it with Geomview's <tt>ndview</tt>. As you
rotate the object in one set of dimensions, you can see how it
changes in other sets of dimensions.</p>

<p>For additional control over 4-d objects, output the object
without 'GDn' and read it with Geomview's <tt>4dview</tt>. You
can slice the object along any 4-d plane. You can also flip the
halfspace that's deleted when slicing. By combining these
features, you can get some interesting cross sections.</p>

<h3><a href="#geomview">&#187;</a><a name="Gh">Gh - display
hyperplane intersections (3-d, 4-d)</a></h3>

<p>In 3-d, the intersection is a black line. It lies on two
neighboring hyperplanes, c.f., the blue squares associated with
centrums ('<a href="#Gc">Gc</a>'). In 4-d, the ridges are
projected to the intersection of both hyperplanes. If you turn on
edges (Geomview's 'appearances' menu), each triangle corresponds
to one ridge. The ridges may overlap each other.</p>

<h3><a href="#geomview">&#187;</a><a name="Gi">Gi - display inner
planes only (2-d, 3-d)</a></h3>

<p>The inner plane of a facet is below all of its vertices. It is
parallel to the facet's hyperplane. The inner plane's color is
the opposite of the outer plane's color, i.e., <i>[1-r,1-g,1-b] </i>.
Its edges are determined by the vertices.</p>

<h3><a href="#geomview">&#187;</a><a name="Gn">Gn - do not display planes</a></h3>

<p>By default, Geomview displays the precise plane (no merging)
or both inner and output planes (if merging). If merging,
Geomview does not display the inner plane if the the difference
between inner and outer is too small.</p>

<h3><a href="#geomview">&#187;</a><a name="Go">Go - display outer
planes only (2-d, 3-d)</a></h3>

<p>The outer plane of a facet is above all input points. It is
parallel to the facet's hyperplane. Its color is determined by
the facet's normal, and its edges are determined by the vertices.</p>

<h3><a href="#geomview">&#187;</a><a name="Gp">Gp - display coplanar
points and vertices as radii</a></h3>

<p>Coplanar points ('<a href="qh-optq.htm#Qc">Qc</a>'), interior
points ('<a href="qh-optq.htm#Qi">Qi</a>'), outside points ('<a
href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TVn">TVn</a>'),
and vertices are displayed as red and yellow radii. The radii are
perpendicular to the corresponding facet. Vertices are aligned
with an interior point. The radii define a ball which corresponds
to the imprecision of the point. The imprecision is the maximum
of the roundoff error, the centrum radius, and <i>maxcoord * (1 -
</i><a href="qh-optc.htm#An">A-n</a><i>)</i>. It is at
least 1/20'th of the maximum coordinate, and ignores post merging
if pre-merging is done.</p>

<p>If '<a href="qh-optg.htm#Gv">Gv</a>' (print vertices as
spheres) is also selected, option 'Gp' displays coplanar
points as radii.  Select options <a href="qh-optq.htm#Qc">Qc</a>'
and/or '<a href="qh-optq.htm#Qi">Qi</a>'. Options 'Qc Gpv' displays
coplanar points while 'Qci Gpv' displays coplanar and interior
points.  Option 'Qc' is automatically selected if 'Qi' is not
selected with options 'Gpv'.

<h3><a href="#geomview">&#187;</a><a name="Gr">Gr - display ridges (3-d)</a></h3>

<p>A ridge connects the two vertices that are shared by
neighboring facets. It is displayed in green. A ridge is the
topological edge between two facets while the hyperplane
intersection is the geometric edge between two facets. Ridges are
always displayed in 4-d.</p>

<h3><a href="#geomview">&#187;</a><a name="Gt">Gt - transparent 3-d Delaunay</a></h3>

<p>A 3-d Delaunay triangulation looks like a convex hull with
interior facets. Option 'Gt' removes the outside ridges to reveal
the outermost facets. It automatically sets options '<a
href="#Gr">Gr</a>' and '<a href="#GDn">GDn</a>'. See example <a
href="qh-eg.htm#17f">eg.17f.delaunay.3</a>.</p>

<h3><a href="#geomview">&#187;</a><a name="Gv">Gv - display vertices
as spheres (2-d, 3-d)</a></h3>

<p>The radius of the sphere corresponds to the imprecision of the
data. See '<a href="#Gp">Gp</a>' for determining the radius.</p>

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